Observational studies are frequently used to compare long-term effects of treatments. Without randomization, patients receiving one treatment are not guaranteed to be prognostically comparable to those receiving another treatment. Furthermore, the response of interest may be right-censored due to incomplete follow-up. Statistical methods that do not account for censoring and confounding may lead to very biased estimates. We review the assumptions required to estimate average causal effects and derive an estimator for comparing two treatments by applying inverse weights to the complete cases. Using martingale representations, the estimator is shown to be asymptotically normal and an estimator for the asymptotic variance is derived. Simulation results are presented to evaluate the properties of the estimator. These methods are applied to an observational database of acute coronary syndrome patients to estimate the effect of a treatment strategy on the mean five-year medical cost.This is joint work with Anastasios A. Tsiatis.
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